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A293319
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Greatest integer k such that k/2^n < tau^2, where tau = (1+sqrt(5))/2 = golden ratio.
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3
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2, 5, 10, 20, 41, 83, 167, 335, 670, 1340, 2680, 5361, 10723, 21446, 42893, 85787, 171575, 343150, 686301, 1372603, 2745207, 5490415, 10980830, 21961660, 43923321, 87846643, 175693286, 351386573, 702773147, 1405546295, 2811092590, 5622185180, 11244370361
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = floor((r*2^n)), where r = (3+sqrt(5))/2.
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MATHEMATICA
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z = 120; r = 1+GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}]; (* A293319 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293320 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293321 *)
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PROG
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(Magma) [Floor((2^n*(3+Sqrt(5)))/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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